Will kill Arya Stark Waif

Why is Arya Stark allowed to do this in the Game of Thrones season six finale? [Duplicate]

This is a multi-part answer as your question is a bit vague.

To give you a quick recap, the most likely in my opinion are:

  • Arya has the skills of faceless men, but is not a faceless man.
  • The versatile God allows Arya to change her face for doing things the MFG likes (even if the MFG isn't the The reason is, why Arya kills who she kills)

A more detailed answer can be found below.

1. Arya is a faceless man

What do you mean when you say that From my point of view there are two possible meanings:

  1. Arya is an active member of the Order of Faceless Men.
  2. Arya has the skills of a faceless man.

1 is wrong. She leaves the faceless men and retains the identity of Arya Stark. However, it is true that they do was invited to become a faceless man (proves to Jaqen that "a girl is finally nobody"), but Arya refused.

2 is true as she kills Walder Frey in disguise and later explicitly states that she has the ability to speak to Sansa.

2. Why can Arya use the faces if she is not a member of the Order?

I think that is what matters with your question.

The faculty of changing faces seems to be twofold. There is one physical Aspect: Arya has to cut off someone's face to wear that face. That physical aspect is one ability that Arya was taught. Just because she leaves the faceless men doesn't mean she has forgotten the skill.

As @BCDotWeb said in the comments:

If you graduated to be a chef, do you then ask permission from the school you graduated from if you make a sandwich?

Arya doesn't need permission to cut off faces. It's not a patented process.

But there is also one magical Aspect. How does this change her body when Arya puts on a face? Why is her voice and demeanor changing (and why, according to the books, does she have the memories of this person?)

This is never really explained (as no magic has really been explained on the show yet). We can only trust the words of Jaqen, who said that God of many things gives them this power.

In other words, Arya can change face because the versatile God has granted this power

From my point of view there are two ways it works. Note that of course this is more speculation than anything, but I'll just try to list every logical possibility.

1. The versatile God has automated the process.

By that I mean that the MFG does not have to "approve" every face change on a case-by-case basis.

We could prove this theory by seeing what happens if someone else steals one of Arya's faces and puts it on. If it changes her, that means , that everyone can change face (which then explains why Arya is able to change face even though she is not a member of the Order).

In either case, it is likely that the face itself will need to be cut in a certain way, what in a ability that Arya learned herself.

2. The process is not automated, the eclectic God advocates that Arya change faces every time she does this.

In other words, the MFG must "approve" each face change on a case-by-case basis.

We could prove this theory by seeing what happens if someone else steals one of Arya's faces and puts it on. If it doesn't change them, it means that only certain people are allowed to change face.

That doesn't make sense at first. Arya is not a member of the Order of Faceless Men. Why should the MFG allow her to switch faces?

Unless the MFG Right Arya's plan too. What if he is aware of the future of Arya (other gods have proven similarly prophetic), knows what Arya will do, and approves of it?
After all, he is the one God of Death , and Arya wants to kill people.

While she is not a faceless man, that does not mean that the MFG still cannot approve of her actions.

Nobody said the MFG just doing faceless men a favor. (Pun not intended)

Likewise, one might wonder why the Lord of Light raised Jon who did not become a devout worshiper (comparatively, Beric became a believer through his resurrection). The simplest explanation is that Jon was resurrected for a good reason independently of Jon's personal beliefs. The Lord of Light doesn't need Jon to preach, he needs Jon to do what he is meant to do.

And if you agree with Jon's example, so can Arya and the versatile God too.